A coupling rod or side rod connects the driving wheel

Driving wheel

On a steam locomotive, a driving wheel is a powered wheel which is driven by the locomotive's pistons...

s of a locomotive

Locomotive

A locomotive is a railway vehicle that provides the motive power for a train. The word originates from the Latin loco – "from a place", ablative of locus, "place" + Medieval Latin motivus, "causing motion", and is a shortened form of the term locomotive engine, first used in the early 19th...

. Steam locomotive

Steam locomotive

A steam locomotive is a railway locomotive that produces its power through a steam engine. These locomotives are fueled by burning some combustible material, usually coal, wood or oil, to produce steam in a boiler, which drives the steam engine...

s in particular usually have them, but some diesel

Diesel locomotive

A diesel locomotive is a type of railroad locomotive in which the prime mover is a diesel engine, a reciprocating engine operating on the Diesel cycle as invented by Dr. Rudolf Diesel...

 and electric

Electric locomotive

An electric locomotive is a locomotive powered by electricity from overhead lines, a third rail or an on-board energy storage device...

 locomotives, especially older ones and shunters

Switcher

A switcher or shunter is a small railroad locomotive intended not for moving trains over long distances but rather for assembling trains ready for a road locomotive to take over, disassembling a train that has been...

, also have them. The coupling rods transfer the power to all the wheels.
Locomotion No 1

Locomotion No 1

Locomotion No. 1 is an early British steam locomotive. Built by George and Robert Stephenson's company Robert Stephenson and Company in 1825, it hauled the first train on the Stockton and Darlington Railway on 27 September 1825....

 was the first locomotive to employ coupling rods rather than chains

Chain drive

Chain drive is a way of transmitting mechanical power from one place to another. It is often used to convey power to the wheels of a vehicle, particularly bicycles and motorcycles...

. In the 1930s reliable roller bearing coupling rods were developed.

The coupling rod's off-center attachment to the outside of the driving wheel inevitably creates an eccentric movement and vibration when in motion.